Problem: Simplify to lowest terms. $\dfrac{80}{70}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 80 and 70? $80 = 2\cdot2\cdot2\cdot2\cdot5$ $70 = 2\cdot5\cdot7$ $\mbox{GCD}(80, 70) = 2\cdot5 = 10$ $\dfrac{80}{70} = \dfrac{8 \cdot 10}{ 7\cdot 10}$ $\hphantom{\dfrac{80}{70}} = \dfrac{8}{7} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{80}{70}} = \dfrac{8}{7} \cdot 1$ $\hphantom{\dfrac{80}{70}} = \dfrac{8}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{80}{70}= \dfrac{2\cdot40}{2\cdot35}= \dfrac{2\cdot 5\cdot8}{2\cdot 5\cdot7}= \dfrac{8}{7}$